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UK pupils will have to keep up maths until they’re 18 (PA)

Currently, here in the UK school pupils are only required to study maths up to the age of 16, but under new plans unveiled by the prime minister, all pupils will have to continue their study of the subject until they’re 18.

Rishi Sunak is expected to say that there is a need to "reimagine our approach to numeracy" in his first speech of the year.

More details of the PM’s "new mission" are to be announced "in due course" but in the meantime, how good are your maths skills?

Here at The Independent we’ve found some example questions from A level Maths past papers to test your numeracy and see what the UK’s teenagers could be in for.

All answers at the bottom. Good luck!

1. The lifetime, L hours, of a battery has a normal distribution with mean 18 hours and standard deviation 4 hours. Alice’s calculator requires 4 batteries and will stop working when any one battery reaches the end of its lifetime. Find the probability that a randomly selected battery will last for longer than 16 hours.

2. Helen believes that the random variable C, representing cloud cover from the large data set, can be modelled by a discrete uniform distribution. Write down the probability distribution for C.

3. f(x) = 3x3 + 2ax2 – 4x + 5a Given that (x + 3) is a factor of f(x), find the value of the constant a.

4. A competitor is running a 20 kilometre race. She runs each of the first 4 kilometres at a steady pace of 6 minutes per kilometre. After the first 4 kilometres, she begins to slow down. In order to estimate her finishing time, the time that she will take to complete each subsequent kilometre is modelled to be 5% greater than the time that she took to complete the previous kilometre. Estimate the total time, in minutes and seconds, that she will take to complete the race.

5. The line l 1 has equation 2x + 4y – 3 = 0 The line l 2 has equation y = mx + 7, where m is a constant. Given that l 1 and l 2 are perpendicular, find the value of m.

6. A company started mining tin in Riverdale on 1st January 2019. A model to find the total mass of tin that will be mined by the company in Riverdale is given by the equation T = 1200 – 3(n – 20)2 where T tonnes is the total mass of tin mined in the n years after the start of mining. Using this model, calculate the mass of tin that will be mined up to 1st January 2020.

7. A circle C has equation x2 + y2 – 4x + 8y – 8 = 0. Find the coordinates of the centre of C.

8. The value of a car, £V, can be modelled by the equation V = 15 700e– 0.25t + 2300 t \, t . 0 where the age of the car is t years. Using the model, find the initial value of the car.

9. A chocolate manufacturer places special tokens in 2 per cent of the bars it produces so that each bar contains at most one token. Anyone who collects 3 of these tokens can claim a prize. Andreia buys a box of 40 bars of the chocolate. Find the probability that Andreia can claim a prize.

10. A spinner can land on red or blue. When the spinner is spun, there is a probability of 1/3 that it lands on blue. The spinner is spun repeatedly. The random variable B represents the number of the spin when the spinner first lands on blue. Find P(B = 4).

Questions taken from Pearson exam past papers.

1. 0.691, 2. – 0.6215, 3. 3, 4. 173 minutes and 3 seconds, 5. m = 2 or y = 2x + 7, 6. 117 tonnes, 7. 2, -4, 8. £18 000, 9. 0.04567, 10. 0.0988